A common complication for routing in mobile sensor networks is how to efficiently control the forwarding behaviors of relay nodes so as to save their energy consumption and buffer usage while simultaneously satisfy the specified delivery performance requirement. Available works either assign each message with a lifetime, a maximum number of copies, or a sequence number, or flush special feedback information among the whole network after the message reception. In the former case, a relay node has no idea of the message reception status and will carry and forward the message until meeting the destination, while the latter could efficiently notify all relay nodes but demands extra communication resources. Different from previous studies, we consider in this paper an explicit probabilistic stopping mechanism for relay nodes. Under such mechanism, a relay node that is actively disseminating a message will stop spreading the message with a certain probability, after meeting another node having already received the message. We first develop a two-dimensional Markov chain framework to characterize the highly complicated dynamics until the end of message propagation, then conduct Markovian analysis to derive the associated important performance metrics, including the average time required for the completion of message propagation, the expectation and variance of the fraction of nodes finally receiving the message, and the probability that a given number of nodes end up with the message, etc. Finally, extensive numerical results are provided to analytically explore how the network parameter settings may affect these performance metrics.